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• W2038586278 abstract "Abstract We have obtained escape-speed diagrams for a conservative one-parameter quadratic mapping of the plane to itself (the Cremona Map). The escape speed of orbits appears to have a fractal distribution (in the plane) which is related to the eigenvectors of the mapping in the vicinity of the unstable fixed point. We suggest that this phenomenon is due to stability enhancements caused by the stable manifold as it traverses the plane. Since our charts allow classification of regions in the plane by their escape speed, the method actually provides a means of tracking the stable manifold directly. Numerical results indicate that the sections of the manifolds from longer period points extending into the escaping region accumulate onto the stable manifold of the unstable fixed point. An overall stability analysis as the parameter of the mapping is varied shows a remarkable resemblance to the corresponding diagram for the Restricted Three Body Problem, which we discuss briefly." @default.
• W2038586278 created "2016-06-24" @default.
• W2038586278 creator A5042133979 @default.
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• W2038586278 date "1987-11-01" @default.
• W2038586278 modified "2023-10-11" @default.
• W2038586278 title "Fractal distributions in conservative systems: Direct observations of the stable manifold" @default.
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• W2038586278 doi "https://doi.org/10.1016/0167-2789(87)90048-0" @default.
• W2038586278 hasPublicationYear "1987" @default.
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